On the Nature of Space and Time

Abstract

A framework to define the initial conditions of the universe starts with the Planck base units of length, time, mass and charge. It employs multiplication by 2 and defines a natural inflation from the Planck units to the Age of the Universe within just 202 doublings. Recognizing the initial role of pi as the beginning of the basic mathematics, each new prime introduces a natural progression of mathematical complexity and systems throughout all these doublings that inscribe our universe.

I. Introduction

The Planck base units were conceived by Max Planck in 1899 and were first published in 1906. Ignored by most scholars for about 100 years, Frank Wilczek (MIT, Nobel laureate 2004) published a series of three articles in 2001 in Physics Today, Scaling Mt. Planck I, II, III, that pulled them out of obscurity and into discussions within the general academic enterprise.

In December 2011 in the process of following embedded geometries within simple structures, the question was asked, “How far within can we go?” The Planck base units were introduced and it became a simple mathematical and geometrical goal of the high school classes. Within just 45 divisions by 2, the CERN-scale was in views. In another 67 steps, the class was down within the Planck scale. Again, using the power of 2, multiplying the two objects, in just 90 steps, a simple framework for the universe was complete. A chart was developed that followed just the Planck Length (FIG. 1a. Four charts – below). There were just 202 notations in total.

The first 67 notations presented an immediate challenge. The question was asked, “What could be in there?” Too small for fundamental particles as understood today, generalized guesses were made by looking through the history of scholarship. The next chart to emerge was called the Universe Table (FIG. 1b. Four charts).

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* email: camber@81018.org** First Draft, July 4, 2017

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By 2015 the initial chart had been expanded to include Planck Time, Mass, and Charge (FIG. 1c. Four charts). Recognizing that Planck Temperature had been conceptually engaged as a footing of the big bang theory, it was given an “odd duck” status within this emergent model. It did not meet the “simplicity” requirement. It was too difficult to understand. Of all the many great scholars who have appealed for simplicity, one statement by John Wheeler became penultimate: “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium – we will all say to each other, how could it have been otherwise?” So, the first idea for this odd duck was simply to reverse order it. It would approach absolute zero degrees Kelvin, but never reach it. It was placed in notation 203, several billion years away, giving us some time to figure it out.

In April 2016, the long vertical chart was revamped as a horizontally-scrolled chart (FIG. 1d. Four charts). It was easier to follow the logic of the numbers. And these charts became the initial framework for our study of the universe.

II. LOGIC

Assigned the objective to construct a universe from scratch, an assumption was that a logic for that construction might be discerned within the simplest, but most ubiquitous concept within pure mathematics. The simple circle and sphere logically seemed to fit that criteria.

Another assumption was that the universe was finite and that the mathematics for infinities were real. The non-ending, non-repeating numbers, pi being the motherload, seemed to establish a bridge to a certain kind of infinity. It was enough to start. Then, all the dimensionless constants and those never-ending, never repeating incommensurables, imaginary numbers, and transcendentals were taken to be bridges between the finite and infinite. So, the continuum was not abandoned and the discrete structure of spacetime became readied for examination.

Further, the first part of Planck’s equation to compute Planck Time was applied to each notation and that value within each notation approximated the speed of light. It was a variable and light was redefined well beyond the visible light spectrum. Space and time were uniquely derivative of light within each notation.

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That bridge again widen with all the definitions of the Planck base units. Every facet of these equations is considered part of the variegation that defines the bridge. Thus the concept of a singularity within finite space-time has been rejected.

Instantons, gravitons, supergravity, and other illusive concepts within science were also understood to be part of the finite-infinite bridge. Ostensibly the bridge became our catchall for anything science did not fully understand.

This outline of the universe, therefor, seemed to require a redefinition of time and space that made each uniquely local by notation. In this emergent model each notation was actively involved with the current definition of this universe and every notation shared in an active definition of every other notation.

This model would require an additional extension of our understanding of a field. The first 67 notations were scalar fields of a different order. Here there were possibilities for very deep perfections — continuities, symmetries, and harmonies.

III. FIELDS

Adding to the ways we understand the nature of fields today — scalar fields, vector fields, spinor fields and tensor fields (including gravitation fields, electromagnetic fields) – would now be as many as 67 notations whereby each manifestation of a field could be perfected and then reach across the other notations as a perfected state within each space-time container.

IV. ANALYSIS

Although we have been looking at this most simple model of the universe since December 2011, it has taken this long to get comfortable enough with the implications of this work to put it out in the public square. Many articles (below) have danced around this logic and the results.

In order to organize all mathematics and geometry and ordering system from the most simple to the most complex was initiated. The simple formula for pi opens close-packing of equal spheres which opens simple Euclidean geometries (see Lattice generation). Three articles currently being developed continues and analysis of this mathematical progression, each originating within a notation defined by a prime number.

We have asked the best of the best for their comments and have received virtually none. At first it was thought that it was too juvenile to even warrant a response. Then it is becoming evident that it was really too different and too simple and too disruptive to warrant a response. So, this article is placed in the public square to beg for a response. Why is it right? Why is it wrong?

People ask, “Why haven’t we seen this model until now?

Planck Units: The four Planck base units were “…properties of nature and not from any human construct.” Yet, these Planck numbers did not command basic respect across the entire scientific community. Not until Wilczek’s (MIT, Nobel laureate 2004) wrote a series of three articles for Physics Today, Scaling Mt. Planck, did I, II, III, these Planck units begin to move beyond numerology into wide-scale acceptability.

By that time, the big bang theory had gained the high ground. Nobody thought to follow simple nested or combinatorial geometries back to the Planck Length. Nobody thought to multiply the Planck units by 2. It took a huge amount of naïveté and almost no knowledge of cosmological models to bias one’s point of view. It also required discounting our commonsense view promulgated by Isaac Newton that space and time are absolute. In so doing, a more relational model as suggested in 1715 by Leibniz was entertained and the model followed the raw numbers.

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What Have We Done Since December 2011?

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